Each point on a curve has at most two control points: one for the curve entering the point and the other for the curve leaving it. On the following curve, the control points are shown for point 2.
These control points determine the tangent directions and magnitudes of the curve through the point.
Two tangent directions may exist at a point: one before the point and the other after it. In the figure, the tangent directions before and after are shown for point 2. Notice that the position of the tangent direction before is away from its control point and the position of the tangent direction after is towards its control point.
You may set the tangent directions before and after the point independently or both together. If they are set together, the curve is smooth relative to its tangents at that point. The figure below shows an example where the tangent direction before is equal to the tangent direction after at point 2.
You may introduce discontinuities on the curve by setting the tangent directions before and after independently.
Tangent magnitudes have a subtler effect than tangent directions. Like tangent directions, these may also be set before and after each point simultaneously or individually. See Curves for further information on how tangent magnitudes change the shape of a curve.